A Double Machine Learning Approach to Combining Experimental and Observational Data

Experimental and observational studies often lack validity due to untestable assumptions. We propose a double machine learning approach to combine experimental and observational studies, allowing practitioners to test for assumption violations and estimate treatment effects consistently. Our framework tests for violations of external validity and ignorability under milder assumptions. When only one assumption is violated, we provide semi-parametrically efficient treatment effect estimators. However, our no-free-lunch theorem highlights the necessity of accurately identifying the violated assumption for consistent treatment effect estimation. We demonstrate the applicability of our approach in three real-world case studies, highlighting its relevance for practical settings.